Error estimate in Polyfit

Hello,

I'm now reading Moler's Numerical Computing with MATLAB. In M file Cencusgui , in section for error estimate, following lines are written.

Why the error is estimated in this way, would you please provide some theoretical explanation ?

% Provide error estimates for censusgui

switch model

case 'polynomial'

if d > 0

V(:,d+1) = ones(size(t));

s = (t-1955)/55;

for j = d:-1:1

V(:,j) = s.*V(:,j+1);

end

[~,R] = qr(V);

R = R(1:d+1,:);

RI = inv(R);

E = zeros(length(x),d+1);

s = (x-1955)/55;

for j = 1:d+1

E(:,j) = polyval(RI(:,j),s);

end

sig = 10; % Rough estimate

e = sig*sqrt(1+diag(E*E'));

errest = [y-e; NaN; y+e];

else

errest = [y-NaN; NaN; y+NaN];

end